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A006157
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a(n+1) = (n-1) a(n) +n.n!.
(Formerly M3950)
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4
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1, 5, 28, 180, 1320, 10920, 100800, 1028160, 11491200, 139708800, 1836172800, 25945920000, 392302310400, 6320426112000, 108101081088000, 1956280854528000
(list; graph; refs; listen; history; internal format)
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OFFSET
| 2,2
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COMMENTS
| Number of ascending runs of length at least two in all permutations of [n]. Example: a(3)=5 because we have (123), (13)2, 3(12), 2(13), (23)1 and 321, where the ascending runs of length at least 2 are shown between parentheses. - Emeric Deutsch and Ira Gessel (deutsch(AT)duke.poly.edu), Sep 07 2004
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REFERENCES
| J. Francon, Histoires de fichiers, RAIRO Informatique Th\'{e}orique et Applications, 12 (1978), 49-62.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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FORMULA
| (2n-1)/6 * n!.
E.g.f. = x^2*(3-x)/[6(1-x)^2]. - Emeric Deutsch and Ira Gessel (deutsch(AT)duke.poly.edu), Sep 07 2004
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CROSSREFS
| Cf. A014484.
Sequence in context: A082031 A020081 A095676 * A179326 A156629 A123776
Adjacent sequences: A006154 A006155 A006156 * A006158 A006159 A006160
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KEYWORD
| nonn,easy
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com), Simon Plouffe (simon.plouffe(AT)gmail.com)
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